Details

Time bar (total: 1.6m)

sample698.0ms

Algorithm
intervals
Results
445.0ms1299×body80nan
148.0ms423×body80valid

simplify5.4s

Counts
1 → 1
Iterations
IterNodes
49507
31091
2188
155
022

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.4b

localize99.0ms

Local error

Found 4 expressions with local error:

6.5b
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
10.3b
(pow (/ d h) (/ 1 2))
11.2b
(pow (/ d l) (/ 1 2))
12.8b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
331×add-exp-log
179×prod-exp
99×div-exp
60×pow-exp
45×times-frac
42×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×add-cbrt-cube
26×pow-unpow unpow-prod-down
18×pow-to-exp
16×associate-*r*
14×rec-exp 1-exp
13×cbrt-unprod
10×pow1
6×prod-diff
5×distribute-rgt-in cbrt-undiv distribute-lft-in div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ associate-*r/
2×sub-neg pow-pow associate-*l* pow-prod-down *-commutative sqr-pow
1×frac-times flip3-- flip--
Counts
4 → 222
Calls
4 calls:
78.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
9.0ms
(pow (/ d h) (/ 1 2))
10.0ms
(pow (/ d l) (/ 1 2))
62.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series720.0ms

Counts
4 → 12
Calls
4 calls:
431.0ms
(* (* (pow (/ d h) (/ 1 2)) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
89.0ms
(pow (/ d h) (/ 1 2))
77.0ms
(pow (/ d l) (/ 1 2))
124.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify10.8s

Counts
234 → 234
Iterations
IterNodes
24293
11343
0461

prune1.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.3b

localize71.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (* M D) (* 2 d))
6.5b
(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
10.3b
(pow (/ d h) (/ 1 2))
12.8b
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

rewrite464.0ms

Algorithm
rewrite-expression-head
Rules
320×add-exp-log
171×prod-exp
96×div-exp
46×add-cbrt-cube pow-exp
28×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
20×cbrt-unprod
16×associate-*r*
14×rec-exp 1-exp
13×pow-unpow unpow-prod-down
11×pow-to-exp
9×pow1 cbrt-undiv associate-*r/
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×frac-times sqrt-div
2×sub-neg flip3-- associate-*l* pow-prod-down *-commutative flip--
1×clear-num associate-/r* pow-pow frac-2neg associate-/l* sqr-pow
Counts
4 → 201
Calls
4 calls:
11.0ms
(/ (* M D) (* 2 d))
363.0ms
(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
12.0ms
(pow (/ d h) (/ 1 2))
72.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

series1.7s

Counts
4 → 12
Calls
4 calls:
39.0ms
(/ (* M D) (* 2 d))
1.4s
(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
110.0ms
(pow (/ d h) (/ 1 2))
131.0ms
(* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))

simplify7.6s

Counts
213 → 213
Iterations
IterNodes
25482
11407
0476

prune1.6s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.5b

localize114.0ms

Local error

Found 4 expressions with local error:

4.1b
(/ (* M D) (* d 2))
4.1b
(/ (* M D) (* d 2))
6.5b
(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
10.3b
(pow (/ d h) (/ 1 2))

rewrite361.0ms

Algorithm
rewrite-expression-head
Rules
61×add-exp-log
37×add-cbrt-cube
29×prod-exp
21×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×times-frac
14×cbrt-unprod
13×pow-unpow unpow-prod-down
11×div-exp
8×cbrt-undiv associate-*r/
7×pow1
6×prod-diff pow-exp
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u div-inv add-log-exp
3×pow-to-exp sqrt-div associate-*r*
2×frac-times clear-num associate-/r* sub-neg frac-2neg flip3-- flip-- associate-/l*
1×pow-pow associate-*l* pow-prod-down associate-*l/ *-commutative sqr-pow
Counts
4 → 132
Calls
4 calls:
11.0ms
(/ (* M D) (* d 2))
12.0ms
(/ (* M D) (* d 2))
330.0ms
(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
6.0ms
(pow (/ d h) (/ 1 2))

series1.6s

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (* M D) (* d 2))
50.0ms
(/ (* M D) (* d 2))
1.4s
(* (* (pow (/ d h) (/ 1 2)) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))
90.0ms
(pow (/ d h) (/ 1 2))

simplify3.4s

Counts
144 → 144
Iterations
IterNodes
24448
1981
0319

prune1.8s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 7.9b

localize146.0ms

Local error

Found 4 expressions with local error:

3.5b
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))
4.1b
(/ (* M D) (* d 2))
4.1b
(/ (* M D) (* d 2))
6.5b
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

rewrite3.2s

Algorithm
rewrite-expression-head
Rules
2511×add-exp-log
1825×add-cbrt-cube
1545×prod-exp cbrt-unprod
703×cbrt-undiv div-exp
78×frac-times
76×associate-*r/
59×associate-*l/
47×pow1
43×associate-*r*
38×times-frac
36×cbrt-prod sqrt-div
32×add-sqr-sqrt *-un-lft-identity pow-prod-down add-cube-cbrt
8×flip3-- flip--
6×prod-diff
5×distribute-rgt-in distribute-lft-in
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×clear-num associate-/r* sub-neg frac-2neg associate-*l* *-commutative associate-/l*
Counts
4 → 692
Calls
4 calls:
2.2s
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))
21.0ms
(/ (* M D) (* d 2))
14.0ms
(/ (* M D) (* d 2))
901.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

series2.3s

Counts
4 → 12
Calls
4 calls:
128.0ms
(* (* 1/2 (* (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))
51.0ms
(/ (* M D) (* d 2))
33.0ms
(/ (* M D) (* d 2))
2.0s
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (* (cbrt d) (cbrt d))) (sqrt (/ (cbrt d) l)))) (- 1 (* (* 1/2 (* (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))) (* (/ (* M D) (* d 2)) (/ (cbrt h) (cbrt l))))) (/ (cbrt h) (cbrt l)))))

simplify18.9s

Counts
704 → 704
Iterations
IterNodes
15116
01497

prune5.3s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 7.1b

regimes2.3s

Accuracy

18.2% (3.5b remaining)

Error of 11.2b against oracle of 7.7b and baseline of 11.9b

bsearch983.0ms

Steps
ItersRangePoint
11
1.3609975312627296e-279
1.2007207904690597e-258
5.63930426562316e-278

simplify18.0ms

Iterations
IterNodes
259
159
044

end0.0ms

sample23.1s

Algorithm
intervals
Results
14.5s37962×body80nan
5.7s12796×body80valid